Active Queue Management Algorithm for TCP Networks with Integral Backstepping and Minimax

  • Zan-Hua LiEmail author
  • Yang Liu
  • Yuan-Wei Jing
Regular Papers Intelligent Control and Applications


A novel active queue management (AQM) approach is considered for a class of TCP network systems in this paper. A sufficient condition is given and the corresponding control is obtained based on integral back-stepping technique (IB) and minimax method. The presented results not only are used to deal with the disturbances produced by UDP flows, but also can shorten the convergent time of the signals. Simulation examples are carried out to verify the effectiveness and superiority of the proposed algorithm.


Active queue management(AQM) congestion control integral backstepping minimax 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    S. Floyd and V. Jacobson, “Random early detection gateways for congestion avoidance,” IEEE/ACM Trans. on Networking, vol. 1, no. 4, pp. 397–413, Aug 1993.Google Scholar
  2. [2]
    F. Kelly, A. Maulloo, and D. Tan, “Rate control for communication networks: shadow prices, proportional fairness and stability,” Journal of the Operational Research Society, vol. 49, no. 3, pp. 237–252, 1998.zbMATHGoogle Scholar
  3. [3]
    F. Kelly, “Mathematical modeling of the internet,” Mathematics Unlimited-2001 and Beyond, pp. 685–702, 2001.Google Scholar
  4. [4]
    C. Liao and Z. Tian, “Effective adaptive virtual queue: a stabilizing active queue management algorithm for improving responsiveness and robustness,” IET Communications, vol. 5, no. 1, pp. 99–109, 2011.MathSciNetzbMATHGoogle Scholar
  5. [5]
    S. Kunniyur and R. Strikant, “An adaptive virtual queue (AVQ) algorithm for active queue management,” IEEE/ACM Transactions on Networking, vol. 12, no. 2, pp. 286–299, 2004.Google Scholar
  6. [6]
    S. Athuraliya, S. Low, and Q. Yin, “REM: active queue management,” IEEE Network, vol. 15, no. 3, pp. 48–53, 2001.Google Scholar
  7. [7]
    V. Misra, W. B. Gong, and D. Towsley, “Fluid-based analysis of a network of AQM routers supporting TCP flows with an application to RED,” Proceedings of ACM/SIGCOMM00, Sweden, pp. 151–160, 2000.Google Scholar
  8. [9]
    M. Azadegan, M. T. H. Beheshti, and B. Tavassoli, “Using AQM for performance improvement of net-worked control systems,” International Journal of Control Automation & Systems, vol. 13, no. 3, pp. 764–772, 2015.Google Scholar
  9. [10]
    Y. Tang, M. Xiao, and G. Jiang, “Fractional-order PD control at Hopf bifurcations in a fractional-order congestion control system,” Nonlinear Dynamics, vol. 90, no. 3, pp. 1–14, 2017.MathSciNetzbMATHGoogle Scholar
  10. [11]
    H. Hamidian and M. T. H. Beheshti, “A robust fractionalorder PID controller design based on active queue management for TCP network,” International Journal of Systems Science, vol. 49, no. 1, pp. 211–216, 2018.MathSciNetzbMATHGoogle Scholar
  11. [12]
    R. Zhu, H. Teng, and J. Fu, “A predictive PID controller for AQM router supporting TCP with ECN,” Lecture Notes in Computer Science, vol. 1, pp. 131–136, 2003.Google Scholar
  12. [13]
    C. W. Feng, L. F. Huang, and C. Xu, “Congestion control scheme performance analysis based on nonlinear RED,” IEEE Systems Journal, vol. 99, pp. 1–8, 2017.Google Scholar
  13. [14]
    S. Xu, M. Fei, and X. Yang, “AQM scheme design for TCP network via TakagiSugeno fuzzy method,” Complexity, vol. 21, no. S2, pp. 606–612, 2016.Google Scholar
  14. [15]
    J. M. Kim, B. P. Jin, and Y. H. Choi, “Wavelet neural network controller for AQMin a TCP net-work adaptive learning rates approach,” International Journal of Control Automation & Systems, vol. 6, no. 4, pp. 526–533, 2008.Google Scholar
  15. [16]
    M. Sheikhan, R. Shahnazi, and E. Hemmati, “Adaptive active queue management controller for TCP communication networks using PSO-RBF models,” Neural Computing and Applications, vol. 22, no. 5, pp. 933–945, 2013.Google Scholar
  16. [17]
    A. Mozo, J. L. López-Presa, and A. F. Anta, “A distributed and quiescent max-min fair algorithm for network congestion control,” Expert Systems with Applications, vol. 91, pp. 492–512, 2018.Google Scholar
  17. [18]
    X. Yang, S. Xu, and Z. Li, “Consensus congestion control in multi-router networks based on multi-agent system,” Complexity, vol. 1, pp. 1–10, 2017.Google Scholar
  18. [19]
    P.Wang, D. Zhu, and X. Lu, “Active queue management algorithm based on data-driven predictive control,” Telecommunication Systems, vol. 64, no. 1, pp. 1–9, 2017.MathSciNetGoogle Scholar
  19. [20]
    Y. Liu, X. Liu, and Y. Jing, “Adaptive backstepping H¥ tracking control with prescribed performance for internet congestion,” ISA Transactions, vol. 72, pp. 92–99, 2018.Google Scholar
  20. [21]
    C. H. Lin, “Nonlinear backstepping control design of LSM drive system using adaptive modified recurrent Laguerre orthogonal polynomial neural network,” International Journal of Control Automation & Systems, vol. 15, no. 2, pp. 905–917, 2017.Google Scholar
  21. [22]
    M. Wang, Z. Zhang, and Y. Liu, “Adaptive back-stepping control that is equivalent to tuning functions design,” International Journal of Control Automation & Systems, vol. 14, no. 1, pp. 90–98, 2016.Google Scholar
  22. [23]
    T. Gao, Y. Liu, L. Liu, and D. Li, “Adaptive neural network-based control for a class of nonlinear purefeedback systems with time-varying full state constraints,” IEEE/CAA Journal of Automatica Sinica, vol. 5, no. 5, pp. 923–933, 2018.MathSciNetGoogle Scholar
  23. [24]
    D. Zhai, L. An, J. Dong, and Q. Zhang, “Switched adaptive fuzzy tracking control for a class of switched nonlinear systems under arbitrary switching,” IEEE Transactions on Fuzzy Systems, vol. 26, no. 2, pp. 585–597, 2018.Google Scholar
  24. [25]
    L. Liu, Y. Liu, and S. Tong, “Neural networks-based adaptive finite-time fault-tolerant control for a class of strictfeedback switched nonlinear systems,” IEEE Transactions on Cybernetics, pp. 1–10, 2018.Google Scholar
  25. [26]
    D. Zhai, L. An, D. Ye, and Q. Zhang, “Adaptive reliable H¥ static output feedback control against Markovian Jumping sensor failures,” IEEE Transactions on Neural Networks & Learning Systems, vol. 29, pp. 631–644, 2018.MathSciNetGoogle Scholar
  26. [27]
    D. Li and D. Li, “Adaptive neural tracking control for an uncertain state constrained robotic manipulator with unknown time-varying delays,” IEEE Transactions on Systems Man&Cybernetics Systems, vol. 48, no. 12, pp. 2219–2228, Dec. 2018.Google Scholar
  27. [28]
    F. J. Niroumand, A. Fakharian, and M. S. Seyedsajadi, “Fuzzy integral backstepping control approach in attitude stabilization of a quadrotor UAV,” Pro.c of 13th Iranian Conference on Fuzzy Systems (IFSC), IEEE, pp. 1–6, 2013.Google Scholar
  28. [29]
    M. Hoshyar and M. Mola, “Full adaptive integral backstepping controller for interior permanent magnet synchronous motors,” Asian Journal of Control, vol. 20, no. 2, pp. 768–779, 2017.MathSciNetzbMATHGoogle Scholar
  29. [30]
    F. Yue, X. Li, and C. Chen, “Adaptive integral backstepping sliding mode control for optoelectronic tracking system based on modified LuGre friction model,” International Journal of Systems Science, vol. 4, pp. 1–8, 2017.Google Scholar
  30. [31]
    Z. Zhou, C. Yu, and K. L. Teo, “Some new results on integral-type backstepping method for a control problem governed by a linear heat equation,” IEEE Transactions on Automatic Control, vol. 62, no. 7 pp. 3640–3645, 2017.Google Scholar
  31. [32]
    M. Guisser, A. El-Jouni, and M. Aboulfatah, et al, “Nonlinear MPPT controller for photovoltaic pumping system based on robust integral backstepping approach,” International Review on Modelling & Simulations, vol. 7, no. 3, pp. 481–488, 2014.Google Scholar
  32. [33]
    M. A. Hamida, J. D. Leon, and A. Glumineau, “High-order sliding mode observers and integral backstepping sensorless control of IPMS motor,” International Journal of Control, vol. 87, no. 10, pp. 2176–2193, 2014.MathSciNetzbMATHGoogle Scholar
  33. [34]
    E. Abolfazli, and V. Shah-Mansouri, “Robust congestion control for TCP/AQM using integral backstepping control,” Proc. of International Symposium on Personal, Indoor, and Mobile Radio Communications, IEEE, pp. 1840–1844, 2015.Google Scholar
  34. [35]
    M. M. Kogan, “Solution to the inverse problem of minimax control and worst case disturbance for linear continuoustime systems,” IEEE Transaction on Automatic Control, vol. 43, no. 5, pp. 670–674, 1998.zbMATHGoogle Scholar
  35. [36]
    D. Motreanu, “On the proof of a minimax principle,” Le Matematiche, vol. 58, no. 1, pp. 95–99, 2003.MathSciNetzbMATHGoogle Scholar
  36. [37]
    J. Moon and T. Baar, “Minimax control over unreliable communication channels,” Automatica, vol. 59, pp. 182–193, 2015.MathSciNetzbMATHGoogle Scholar
  37. [38]
    N. Jiang and Y. W. Jing, “Non-fragile minimax control of nonlinear systems based on T-S model,” Journal of Systems Engineering, vol. 25, no. 5, pp. 925–928, 2008.Google Scholar
  38. [39]
    T. L. Molloy, J. M. Kennedy, and J. J. Ford, “Minimax robust quickest change detection with exponential delay penalties,” IEEE Control Systems Letters, vol. 1, no. 2, pp. 280–285, 2017.Google Scholar
  39. [40]
    H. Habibullah, H. R. Pota, and I. R. Petersen, “A novel application of minimax LQG control technique for highspeed spiral imaging,” Asian Journal of Control, vol. 20, no. 4, pp. 1400–1412, 2017.zbMATHGoogle Scholar
  40. [41]
    L. S. Aragone, J. Gianatti, P. A. Lotito, and L. A. Parente, “An approximation scheme for uncertain minimax optimal control problems,” Set-Valued and Variational Analysis, vol. 2, pp. 1–24, 2017.zbMATHGoogle Scholar
  41. [42]
    S. Zhuk, A. Polyakov, and O. Nakonechnyi, “Note on minimax sliding mode control design for linear systems,” IEEE Transactions on Automatic Control, vol. 62, no. 7, pp. 3395–3400, 2017.MathSciNetzbMATHGoogle Scholar
  42. [43]
    A. K. Hassan, A. S. Mohamed, M. M. Maghrabi, and N. H. Rafat, “Optimal design of one-dimensional photonic crystal filters using minimax optimization approach,” Applied Optics, vol. 54, no. 6, pp. 1399–409, 2015.Google Scholar
  43. [44]
    X. Yuan and Y. Jing, “Research for AQM based on minimax method,” Neural Computing & Applications, vol. 25, no. 7–8, pp. 1755–1760, 2014.Google Scholar
  44. [45]
    M. Sheikhan, R. Shahnazi, and E. Hemmati, “Adaptive active queue management controller for TCP communication networks using PSO-RBF models,” Neural Computing & Applications, vol. 22, no. 5, pp. 933–945, 2013.Google Scholar
  45. [46]
    W. Dong, G. Y. Gu, X. Zhu, and H. Ding, “A high-performance flight control approach for quadrotors using a modified active disturbance rejection technique,” Robotics & Autonomous Systems, vol. 83, pp. 177–187, 2016.Google Scholar

Copyright information

© ICROS, KIEE and Springer 2019

Authors and Affiliations

  1. 1.College of Information Science and Technology, Northeastern University, and School of ScienceShenyang Ligong UniversityShenyangChina
  2. 2.College of Information Science and TechnologyNortheastern UniversityShenyangChina

Personalised recommendations